The state parameter (ψ), representing the difference between a soil’s current and critical void ratios at the same mean effective stress, is a key indicator of soil behaviour. However, traditional methods for estimating ψ from cone penetration test (CPT) data often assume a linear critical state line (CSL), which becomes inaccurate under high overburden stress due to the pronounced non-linearity of the CSL reflecting the onset of significant particle crushing. This study introduces a refined framework based on Bolton’s relative dilatancy index (IR), which inherently accounts for a non-linear CSL and the stress-dependent behaviour of soils. The proposed method integrates relative density derived from CPT data with the soil behaviour type index (Ic), enabling incorporation of sleeve friction data into the analysis for differentiating between soil types. For clean sands (Ic < 1.64), the framework is further enhanced by accounting for compressibility using readily available index properties. Preliminary validation using calibration chamber data and an example application to a field CPT in deep mine tailings indicates the proposed IR-based method provides an improved method for estimating ψ, particularly under high-stress conditions. Importantly, it is stressed that while ψ offers insight into in-situ soil state, it should not be interpreted as a direct measure of liquefaction potential or liquefied strength at high stresses, where soils also tend to become more ductile.
Jensen et al. (2026) studied this question.